Continuous non-invasive blood pressure monitoring method and apparatus

ABSTRACT

A non-invasive apparatus and method for monitoring the blood pressure of a subject detects a pulse signal at both a first and second location on the subject&#39;s body. The elapsed time between the arrival of corresponding points of the pulse signal at the first and second locations is determined. Blood pressure is related to the elapsed time by relationships such as:where a and b are constants dependent upon the nature of the subject and the signal detecting devices. The system can be calibrated by measuring a single pair of reference blood pressure and corresponding elapsed time.

REFERENCE TO RELATED APPLICATION

This application claims the benefit of the filing dates of U.S.provisional patent application No. 60/178,027 filed on Jan. 26, 2000 anda continuation of PCT international application No. PCT/CA00/0152 filedon Dec. 22, 2000 and entitled CONTINUOUS BLOOD PRESSURE MONITORINGMETHOD AND APPARATUS.

FIELD OF THE INVENTION

This invention relates to blood pressure monitoring devices of the typewhich measure transit times of pulses in a subject's blood circulatorysystem and compute an estimated blood pressure from the measured pulsetransit times.

BACKGROUND OF THE INVENTION

Various approaches have been tried for monitoring the blood pressure ofliving subjects. One approach is to insert a pressure sensor directlyinto a suitable artery in the subject. The sensor can be connected to asuitable monitoring device by a lead which passes through the subject'sskin. This approach provides accurate and instantaneous blood pressuremeasurements. A disadvantage of this approach is that it is invasive. Asurgical procedure is required to introduce the pressure sensor. Thefistula through which the lead exits the subject's body can provide apathway for infection.

Another approach to measuring blood pressure uses a sphygmomanometer. Atypical sphygmomanometer has an occluding cuff capable of being wrappedaround a subject's arm; a pump for inflating the cuff; either an aneroidor mercury gravity sphygmomanometer to measure pressure in the cuff; anda stethoscope or other system for detecting Korotkoff sounds. Suchdevices are widely used in hospitals and doctors' offices for makingroutine blood pressure measurements but are not well adapted toproviding continuous blood pressure monitoring.

Another method for measuring blood pressure is the oscillometric method.Oscillometric blood pressure measurements are made by using a transducerto detect and measure pressure waves in a pressure cuff as blood surgesthrough an artery constricted by the pressure cuff. Many currentlyavailable digital blood pressure monitors use the oscillometric methodfor determining blood pressure. The oscillometric method is not idealfor continuous blood pressure monitoring because it typically cannotproduce an updated blood pressure reading more frequently than aboutonce every 30 seconds. Further, the cuff compresses underlying tissues.Over an extended period of time this can cause tissue damage.

There has been significant research directed toward the development ofnew non-invasive techniques for monitoring blood pressure. One approachexploits the correlation between blood pressure and the time taken for apulse to propagate from a subject's heart to a selected point on asubject's artery. This approach is possible because the speed at whichpulse waves travel from the heart to points downstream in a subject'sblood circulatory system varies with blood pressure. As blood pressurerises the propagation velocity of arterial pulse waves increases and thepulse transit time decreases. In general, such methods may be calledPulse Transit Time (or “PTT”) methods. Typically a signal from anelectrocardiogram (EKG) is used to detect a heart beat and a pressuresensor is used to detect the arrival of a pulse wave generated by theheart beat at a downstream location. This approach is described, forexample, by Inukai et al., U.S. Pat. No. 5,921,936. The Inukai et al.system uses an electrocardiogram to detect the start of a heart beat anduses a cuff equipped with a pressure sensor to detect pulse waves. Othersimilar systems are described in Orr at al., European Patent applicationNo. EP0181067. A variation of this approach is described in Golub, U.S.Pat. No. 5,857,975.

One difficulty with PTT blood pressure measurement systems which measureblood pressure as a function of the time between the pulse of an EKGsignal and a detected pulse wave is that there is a delay between theonset of an EKG pulse and the time that the heart actually begins topump blood. This delay can vary significantly in a random way, even inhealthy subjects. Hatschek, U.S. Pat. No. 5,309,916 discloses a methodfor measuring blood pressure by determining the time taken for a pulseto propagate downstream along a single arterial branch. This approacheliminates uncertainties caused by the imperfect correlation between EKGsignals and the delivery of blood by the heart. However, it has thedisadvantage that it can he difficult to arrange two sensors so thatthey can detect a pulse at each of two widely spaced apart locationsalong a single arterial branch.

Another difficulty with prior art PTT blood pressure measurements isthat the relationship between blood pressure and the time taken forpulses to transmit a portion of the blood circulatory system isdifferent for every subject. Thus, it is necessary to calibrate a PTTblood pressure measurement system for each subject.

The book entitled Monitoring in Anesthesia and Critical Care Medicine,3rd Edition, edited by Blitt and Hines, Churchill Livingstone, 1995,mentions a blood pressure monitor having the trade name, ARTRAC™ 7000which used two photometric sensors, one on the ear and another on afinger, to measure diastolic blood pressure. This device apparently usedthe difference in arrived times of pulses at the ear and finger tomeasure the pulse transit time. The diastolic pressure was estimatedbased on a relationship of pressure and pulse wave velocity. This deviceapparently computed systolic pressure from the pulse volume. Furtherinformation about this device is provided in a FDA 510(k) Notificationentitled, “ARTRAC™ Vital Sign Monitor, Models 7000 and 5000 (K904888),”submitted by Sentinel Monitoring, Inc., 1990.

A relationship between blood pressure and pulse transit time can bedeveloped by assuming that an artery behaves as if it were a thin-walledelastic tube. This relationship, which is known as theMoens-Korteweg-Hughes equation is described in more detail below. TheMoens-Korteweg-Hughes equation depends on the elasticity and geometry ofblood vessels and is highly nonlinear.

Inventors Aso et al., U.S. Pat. No. 5,564 427, proposed the use of alinear equation to calculate blood pressure using the EKG based pulsetransit time. This method was further developed by Hosaka et al., U.S.Pat. No. 5,649,543. To calibrate the linear measurement system, Sugo etal., U.S. Pat. No. 5,709,212, introduced a multi-parameter approach todetermine the parameters at deferent blood pressure levels for systolicand diastolic pressures respectively. Shirasaki patented another methodto calibrate the parameters based on the multiple blood pressurereference inputs in Japanese patent No. 10-151118.

Despite progress that has been made in the field of blood pressuremeasurement, there remains a need for devices for blood pressuremeasurement which have acceptable accuracy and do not requirecomplicated calibration steps.

SUMMARY OF THE INVENTION

This invention provides blood pressure measurement methods and apparatuswhich avoid some of the disadvantages of the prior art. Preferredembodiments of the invention are suitable for continuous non-invasiveblood pressure (“CNIBP”) monitoring.

One aspect of the invention provides methods for monitoring bloodpressure. The method comprises detecting a first pulse signal at a firstlocation on a subject and detecting a second pulse signal at a secondlocation on the subject; measuring a time difference betweencorresponding points on the first and second pulse signals; and,computing an estimated blood pressure from the time difference.

In preferred embodiments of the invention, computing an estimated bloodpressure comprises performing the calculation:

P=a+bln(T)

where P is the estimated blood pressure, a is a constant, b is aconstant, and T is the time difference. Most preferably, the constants aand b for a particular subject are determined by performing acalibration by taking a reference blood pressure reading to obtain areference blood pressure P₀, measuring the elapsed time T₀ correspondingto the reference blood pressure and determining values for both of theconstants a and b from P₀ and T₀.

Accordingly, a method for monitoring blood pressure according to oneaspect of the invention comprises; detecting a first pulse signal at afirst location on a subject and detecting a second pulse signal at asecond location on the subject; measuring a reference blood pressure P₀and a corresponding time difference T₀ between the first and secondpulse signals; from the reference blood pressure and corresponding timedifference, determining a first plurality of constant parameters in amulti-parameter equation relating blood pressure and thetime-difference; monitoring the subject's blood pressure by periodicallymeasuring a time difference T between the first and second pulsesignals; computing an estimated blood pressure, P, from the timedifference, T, using the multi-parameter equation and the firstplurality of constant parameters.

The multi-parameter equation may be the calculation:

P=a+b ln(T)

or a mathematical equivalent thereof where a and b are constants.

In some specific embodiments, determining the plurality of constantparameters in the multi-parameter equation comprises performingcalculations mathematically equivalent to:$a = {c_{1} + \frac{c_{2}\left( {P_{0} - c_{1}} \right)}{{\ln \left( T_{0} \right)} + c_{2}}}$${and},{b = \frac{P_{0} - c_{1}}{{\ln \left( T_{0} \right)} + c_{2}}}$

to obtain values for the constants a and b, where c₁ and c₂ arepredetermined constants.

In other specific embodiments of the invention determining the pluralityof constant parameters in the multi-parameter equation comprisesperforming calculations mathematically equivalent to:

a=P ₀−(c ₃ T ₀ +c ₄)ln(T ₀),

and

b=c ₃ T ₀ +c ₄

where a and b are first and second parameters and c₃ and c₄ arepredetermined constants.

In preferred embodiments of the invention the multi-parameter equationcomprises a non-linear function which is monotonically decreasing andconcave upward in a manner specified by the constant parameters.

The invention may be applied to measuring systolic blood pressures ofsubjects. In preferred embodiments of the invention measuring the timedifference T comprises measuring a first time difference T_(S) forhigher portions (ie portions corresponding generally to the parts of thesignals associated with systolic blood pressure) of the first and secondsignals. Measuring the first time difference may comprise maximizing across-correlation between the first and second pulse signals.Preferably, in such measurements portions of the first and second pulsesignals below a first threshold are not considered. The first thresholdmay be an average value for the signal (or equivalently a mean value forthe signal).

Another aspect of the invention provides a method for estimating a bloodpressure of a subject. The method comprises detecting a pulse signal ata first location; detecting the pulse signal at a second location;determining an elapsed time, T, between the arrival of correspondingpoints of the pulse signal at the first and second locations; and,computing an estimated blood pressure, P, from the elapsed time byperforming the calculation:

P=a+b ln(T)

where a and b are constants.

Yet another aspect of the invention provides a method for estimating theblood pressure, P, of a subject. The method comprises: detecting a firstpulse signal at a first location; detecting a second pulse signal at asecond location; performing a calibration by measuring the subject'sblood pressure P₀ and measuring a corresponding elapsed time, T₀,between the arrival of corresponding points of the first and secondpulse signals; subsequently monitoring the subject's blood pressure bydetermining an elapsed time, T, between the corresponding points of thefirst and second pulse signals; and, calculating an estimated bloodpressure, P, based on the value:$\frac{\left( {P_{0} - c_{1}} \right)}{\left( {{\ln \left( T_{0} \right)} + c_{2}} \right)}$

where c₁ and c₂ are constants.

A still further aspect of the invention provides a method for estimatingthe blood pressure, P, of a subject. The method comprises: detecting afirst pulse signal at a first location; detecting a second pulse signalat a second location; performing a calibration by measuring thesubject's blood pressure P₀ and measuring a corresponding elapsed time,T₀, between corresponding points of the first and second pulse signals;subsequently monitoring the subject's blood pressure by determining anelapsed time, T, between corresponding points of the first and secondpulse signals; and, calculating an estimated blood pressure, P,substantially according to the equation:

P=P ₀=(c ₃ T ₀ +c ₄)ln(T/T ₀)

where c₃ and c₄ are constants.

Yet another aspect of the invention provides a method for estimating theblood pressure, P, of a subject. The method comprises: detecting a firstpulse signal at a first location; detecting a second pulse signal at asecond location; measuring a reference blood pressure P₀ and measuring acorresponding time difference, T₀, between corresponding points of thefirst and second pulse signals; from the reference blood pressure andcorresponding time difference, determining a plurality of constantparameters in a multi-parameter equation relating blood pressure and thetime difference by: determining a first parameter of the plurality ofparameters as a predetermined function of the corresponding timedifference; and, determining a second parameter of the plurality ofparameters as a predetermined function of the reference blood pressureand the time difference; and, subsequently monitoring the subject'sblood pressure by determining a time difference, T, betweencorresponding points of the first and second pulse signals and computingan estimated blood pressure from the time difference T using themulti-parameter equation and the first and second parameters.

Other aspects of the invention provide apparatus for making bloodpressure measurements. One such aspect of the invention providesapparatus for estimating a blood pressure of a subject. The apparatuscomprises a computer processor; an input for receiving a first signalcorresponding to a pulse signal detected at a first location; an inputfor receiving a second signal corresponding to the pulse signal detectedat a second location; a program store containing computer softwarecomprising instructions which, when run on the processor cause theprocessor to measure an elapsed time, T, between corresponding points onthe first and second signals and compute an estimated blood pressure, P,from the elapsed time by performing the calculation:

P=a+b ln(T)

where a and b are constants.

Another apparatus-related aspect of the invention provides apparatus forestimating a blood pressure of a subject. The apparatus comprises:signal detection means for detecting first and second pulse signals;correlation means for determining an elapsed time, T, between the firstand second pulse signals; computation means for computing an estimatedblood pressure, P, from the elapsed time according to a non-linearfunction which is generally decreasing and concave upward in a mannerspecified by two or more settable parameters; calibration means forreceiving a reference blood pressure and associating the reference bloodpressure with an elapsed time determined by the correlation means; and,means responsive to the calibration means for establishing values forthe two or more settable parameters from the reference blood pressureand elapsed time.

A still further aspect of the invention provides a program productcomprising a medium bearing computer-readable signals. The signalscontain instructions which, when executed on a computer processor, causethe computer processor to perform a method according to the invention.

Further advantages and features of the invention are described below.

BRIEF DESCRIPTION OF THE DRAWINGS

In drawings which illustrate non-limiting embodiments of the invention:

FIG. 1 is a block diagram of apparatus according to the invention;

FIG. 2 is a diagram illustrating first and second pulse signals detectedby the apparatus of FIG. 1;

FIG. 3 is a block diagram of apparatus according to one specificembodiment of the invention;

FIG. 4 is a schematic diagram of a possible sensor andsignal-conditioning circuit for use in the invention;

FIG. 5 is a plot of two constants a and b in a formula for estimatingsystolic blood pressure used in a preferred embodiment of the invention;

FIG. 6 is a plot of two constants a and b in a formula for estimatingdiastolic blood pressure used in a preferred embodiment of theinvention;

FIG. 7 is a plot illustrating a relationship between the constant b andT which may be taken advantage of in calibrating apparatus according tothe invention for measuring systolic blood pressures;

FIG. 8 is a plot illustrating a relationship between the constant b andT which may be taken advantage of in calibrating apparatus according tothe invention for measuring diastolic blood pressures;

FIG. 9 is a flow chart illustrating a computer-implemented method forestimating blood pressure according to the invention;

FIG. 10 illustrates a possible organization for software for use in theinvention; and,

FIG. 11 is a view of a possible user interface display for use in theinvention.

DETAILED DESCRIPTION

The methods of the invention use the difference in transit times ofpulse waves to different points on a subject's anatomy to measure bloodpressure As such, such methods may be called differential pulse transittime (“DPTT”) methods FIG. 1 shows a blood pressure monitoring system 10according to the invention. System 10 has an input sub-system comprisingfirst and second sensors 12 and 14 which are each capable of detecting apulse signal at a location on a subject. FIG. 2 depicts typical pulsesignals 16 and 18. Sensors 12 and 14 can advantageously be photoelectricpulse wave sensors on a type used for pulse oximetry. An example of sucha sensor is the model SAS-F FingerSat™ sensor available fromDatex-ohmeda (Canada) Incorporated. Sensors of this type are easy toobtain, reasonable in cost, light in weight and familiar to medicalprofessionals.

Other types of sensor capable of detecting the arrivals of pulse wavesat a location on a subject may also be used within the broad scheme ofthe invention. For example, FIG. 4 is a schematic diagram of a specificsensor implementation in which an OP140A light emitting diode availablefrom Optech Technology Inc. is used to generate light. The light isreflected back to a model OP550A phototransistor also available fromOptech Technology Inc. The remaining circuitry shown in FIG. 4 is anexample of one possible embodiment for signal conditioning circuitrywhich could be used in the practice of this invention.

Other types of sensors which are capable of generating a signalrepresenting the arrivals of pulses at different locations on asubject's body could also be used. Some examples of such other types ofsensors are ultrasound sensors, tonometric sensors, and oscillometriccuffs.

Sensors 12 and 14 are applied to first and second locations L1 and L2 ona subject P. In the example illustrated in FIG. 1, L1 is an earlobe ofthe subject and L2 is a finger of the subject. L1 and L2 may be anyplaces on a subject where pulse signals can be readily detected bysensors 12 and 14 respectively L1 and L2 should be chosen so that apulse wave (which originates at the subject's heart) takes a differentamount of time to propagate to L1 than the pulse wave takes to propagateto L2. L1 and L2 can conveniently each be any of a finger, a toe, awrist, an earlobe, an ankle, a nose, a lip, or any other part of thebody where blood vessels are close to the surface of the skin. Mostpreferably, L1 and L2 are the paired combination of:

an earlobe and a finger;

an earlobe and a toe; or,

a finger and a toe.

In preferred embodiments of the invention, L1 and L2 are supplied byblood from different branches of the subject's arterial system so thatL1 is not directly downstream from L2 and L2 is not directly downstreamfrom L1.

Since locations L1 and L2 do not need to be supplied by blood by thesame branch of a subject's arterial system, this invention provides amuch wider and more convenient range of locations for the application ofsensors 12 and 14 than would be the case if sensor 12 was required to bedirectly upstream or downstream from sensor 14.

First and second electrical signals 15 and 17 are generated at sensors12 and 14 respectively. Signals 15 and 17 are respectively conditionedby signal conditioning circuits 20 and 22. Signal conditioning circuits20 and 22 preferably include low-pass filters to eliminate spuriousspikes, noise filters to eliminate interference from power supplies andother noise sources, and gain amplifiers. After being conditioned, firstand second signals 16 and 18 are digitized by an analog-to-digitalconverter (“ADC”) 24. A single ADC 24 may be used to digitize bothsignals 16 and 18. Separate ADC's could also be used for signals 16 and18.

Preferably each of signals 16 and 18 is sampled at a frequency of about1 kHz, or greater. Most preferably the sampling frequency is 2 kHz orgreater. If a sampling frequency of less than 1 kHz is used,interpolation of the sampled data is preferred used to achieve aneffective sampling resolution of 1 millisecond or higher. ADC 24 canconveniently comprise an ADC integrated with a processor 24A capable offorwarding digitized signals 16 and 18 to data processing device 26through a suitable data communication interface 25 for further analysis.For example, ADC 24 may comprise the 8/10 bit ADC portion of a MotorolaMC68HC916X1 microcontroller.

FIG. 2 shows first and second signals 16 and 18. The digitized signalsare provided to a data processing device 26. Data processing device 26may comprise, for example, a programmable device which obtains anestimated blood pressure from characteristics of first and secondsignals 16 and 18. Data processing device 26 may comprise acomputer/microcontroller/microprocessor/DSP or the like connected to ADC24 by a suitable interface 25.

FIG. 3 illustrates apparatus according to a specific embodiment of theinvention wherein interface 25 comprises an RS-232 serial interfacewhich receives digitized data from a Motorola MC68HC916X1microcontroller and transmits that data over a data connection, whichmay comprise, for example, a standard RS-232 serial cable to the serialport of a data processing device 26. Data processing device 26 maycomprise a standard personal computer. In the embodiment of FIG. 3, thepersonal computer is programmed to perform the steps necessary toprocess digitized signals 16 and 18 to yield estimated blood pressurevalues. In typical commercial embodiments of the invention processingdevice 26 is integrated with other parts of system 10 within a commonhousing and may comprise an embedded processor.

Data processing device 26 determines the time separating selectedcorresponding locations on the first and second signals 16 and 18.Preferably, processing device 26 determines both the time differenceT_(S) between the peaks of signals 16 and 18 for use in systolic bloodpressure estimation and the time difference T_(D) between the valleys ofthe first and second signals 16 and 18 for use in diastolic bloodpressure estimation.

There are numerous ways in which T_(S) and T_(D) can be measured. Apreferred method is to use a cross correlation technique. Where twosignals are respectively given by p₁(t) and p₂(t) the correlationbetween the two signals for a time difference of N sample points can beexpressed as follows: $\begin{matrix}{{C_{p1p2}(m)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - m - 1}\quad {{p_{1}(n)}{p_{2}\left( {n + m} \right)}}}}} & (1)\end{matrix}$

The time difference between corresponding points on the two signals isdetermined by finding the value of m for which the correlation C ismaximized and then multiplying by the sampling time Δt (e.g. the timebetween subsequent samples of each signal) as follows:

T=m| _(C max) Δt  (2)

The sampling time Δt may be, for example, 1 millisecond. The samplingtime is determined by the sampling frequency.

In general, T_(S) and T_(D) are different. One way to separately measureT_(S) and T_(D) is to create from signals 16 and 18 a first set ofsignals p₁(t) and p₂(t) which include the peaks of signals 16 and 18 butdo not include the valleys of signals 16 and 18. The cross-correlationbetween the first set of signals can then be used to obtain a value forT_(S). Similarly, a second set of signals p₁(t) and p₂(t) which includethe valleys of signals 16 and 18 but do not include the peaks of signals16 and 18 can be cross-correlated to obtain a value for T_(D). Thevalues for T_(S) and T_(D) can be used as described below to computesystolic and diastolic blood pressures, respectively.

The first set of signals can be created from signals 16 and 18, forexample, by selecting a threshold for each of signals 16 and 18 witheach threshold being lower than the peak values of the signal andsetting to a fixed value, such as zero, all data points having valueslower than the threshold. A suitable threshold may be derived, forexample, by computing the average values of the data points of each ofsignals 16 and 18 and using these average values as thresholds. Meanvalues of signals 16 and 18 could also be used as thresholds and may beconsidered, for the purpose of this disclosure, to be a type of averagevalue.

The second set of signals can be created from signals 16 and 18, forexamples by selecting a threshold for each of signals 16 and 18 witheach threshold being higher than the minimum values of the signal andsetting to a fixed value, such as zero, all data points having valuesgreater than the threshold. A suitable threshold may be derived, forexample, by computing the average or mean values of the data points ofeach of signals 16 and 18 and using the average values as thresholds Thesame or different thresholds may be used in obtaining the first andsecond sets of signals.

The values T_(S) and T_(D) may be obtained from signals 16 and 18 bymethods other than computing correlations between signals 16 and 18. Forexample, peaks or valleys of signals 16 and 18 may be determined byso-called “landmark detection” techniques. Some example landmarkdetection techniques which may be used in the invention are described inSchneider et al, “A noninvasive EMG technique for investigating theexcitation propagation in single motor units,” EMG ClinicalNeurophysiology, Vol. 29, pp.273-250, 1989 which is incorporated hereinby reference.

Times T_(S) and T_(D) may be used to compute an estimate of a subject'sblood pressure. The speed at which pulse waves propagate through asubject's arterial system is related to blood pressure by an equationknown as the Moens-Kortweg-Hughes Equation. L. A. Geddes, Handbook ofBlood Pressure Measurement, Human Press, Clifton, N.J., 1990 describesthe theoretical basis for the variation in pulse propagation speed withblood pressure.

The Moens-Kortweg-Hughes Equation can be expressed as follows:$\begin{matrix}{v = {\sqrt{\left. {{tE}_{0}/\rho}\quad d \right)e^{\lambda \quad P}} = \frac{L}{T}}} & (3)\end{matrix}$

where v is the pulse wave velocity; t is the thickness of the vesselwall; E₀ is the zero-pressure modulus of the vessel wall; ρ is thedensity of blood; d is the diameter of the vessel; λ is a constant thatdepends on the elasticity of the vessel; P is a blood pressure withinthe vessel; L is the distance travelled by a pulse between two points atwhich a pulse is detected; and T is the time elapsed between detectingthe pulse at a first measurement point and detecting the pulse at asecond measurement point.

The Moens-Kortweg-Hughes Equation includes a large number of factorswhich depend upon the elasticity and geometry of a subject's bloodvessels. Many of those who have attempted to measure blood pressure bymeasuring the propagation times of pulse waves have assumed that, over arelevant range, the Moens-Kortweg-Hughes Equation could be expressed asa linear equation. That is, they have assumed that blood pressure andtime are related by the following equation over a relevant range ofpropagation times:

P=AT+B  (4)

where P and T are as defined above and A and B are parameters which arespecific to each individual subject. While the relationship of equation(4) may be used in certain embodiments of this invention, it is notpreferred. One problem is that equation (4) generally leads toinaccurate blood pressure estimates in case, where a subject experienceslarge dynamic fluctuations in blood pressure as can occur in operatingroom situations.

The inventors have discovered that, for purposes of estimating bloodpressure, it is desirable to express the relationship between bloodpressure and elapsed time between detecting pulse signals at twolocations L1 and L2 by way of a non-linear function. The non-linearfunction is preferably generally decreasing and is most preferablymonotonically decreasing with increases in T. The non-linear function ispreferably concave upward and is preferably specified by a pair of twoparameters which can both be adjusted for purposes of calibration. In apreferred embodiment of the invention the non-linear function isgenerated by the following equation:

P=a+b ln(T)  (5)

where P and T are as defined above and a and b are a pair of parametersto be determined for each individual subject by performing acalibration.

The inventors have discovered that the use of a function according toequation (5) for estimating blood pressure provides advantages overmethods which use equation (4) for calculating an estimated bloodpressure.

In order to use either of equations (4) and (5) to estimate the bloodpressure P of a subject from a time difference T it is necessary toobtain values for the constants which are appropriate to the individualin question. Each of equations (4) and (5) includes two constants.

One way to calibrate system 10 for a specific individual is to makemeasurements of both time T and the subject's blood pressure P (using analternative blood pressure measurement device such as sphygmomanometeror automatic blood pressure measurement device) at two times when thesubject's blood pressure is different. At least two measurements arerequired. This yields two equations which can be solved to obtain theconstants a and b for A and B).

Obtaining measurements of T at times when a subject has different bloodpressures is inconvenient. In general a subject's blood pressure willnot predictably fluctuate through a large enough range to obtainmeasurements of T at two different blood pressures within a convenienttime.

Various techniques can be used to deliberately alter a subject's bloodpressure to obtain two points from which values for the constants a andb (or A and B) can be determined. These include: administering drugs tothe subject which have the effect of raising or lowering the subject'sblood pressure (i.e. vasoactive drugs) by taking measurements both whena limb of the subject is in a raised position (so that the basehydrostatic pressure within the subject's blood circulatory system isincreased) and in a lowered position (so that the base hydrostaticpressure within the subject's circulatory system is decreased); orcausing the subject to increase the pressure within his or her thoraciccavity by attempting to exhale against a resistance, as described byInukai et al. U.S. Pat. No. 5,921,926. While all of these techniques maybe used in some embodiments of the invention, none is ideal.

Clinical trials have been conducted to determine the values a and b ofEquation (5). The parameters a and b were experimentally measured for anumber of subjects. This can be done, for example, by measuring thesubject's blood pressure and pulse transit time at a number of differenttimes as the subject's blood pressure varies. Then one can fit the curveof Equation (5) to the data points for each subject to directly obtainvalues for a and b for that subject. The inventors have discovered thata and b are related generally linearly to one another by the equation:

a=c ₁ +c ₂ b  (6)

where c₁ and c₂ are constants. c₁ and c₂ are different for systolic anddiastolic blood pressure measurements. A plot of the values of a and bfor systolic blood pressure measurements made on a number of subjects isshown in FIG. 5. A plot of the values of a and b for diastolic bloodpressure measurements made on a number of subjects is shown in FIG. 6.

By taking advantage of the unexpected relationship between a and b, ablood pressure measurement apparatus according to this invention may becalibrated for a specific person using only one set of measurements.Combining equations (5) and (6) gives the relationships:

P _(S) =c _(1S) +c _(2S) b _(S) +b _(S)ln(T _(S))  (7)

where P_(S) is estimated systolic blood pressure; and,

 P _(D) =c _(1D) +c _(2D) b _(D) +b _(D) ln(T _(D))  (8)

where P_(D) is estimated diastolic blood pressure. The sets of constantsb_(S), C_(1S), C_(2S), and b_(D), C_(1D), C_(2D) in equations 7) and (8)are for systolic and diastolic blood pressures respectively. In general,in this disclosure, the subscript S refers to systolic blood pressureand the subscript D refers to diastolic blood pressure.

For systolic blood pressure it has been determined that c_(1S) andc_(2S) are respectively about 85.41 and −4.73 whereas, for diastolicblood pressure, c_(2D) and c_(2D) are respectively about 49.36 and −4.30when blood pressure is expressed in mmHg, and PTT or DPTT is expressedin milliseconds. Although it is considered best to use the foregoingvalues, in methods and apparatus of the invention the specific valuesused for the constants c_(1S) and c_(2S), c_(1D) and c_(2D) may bevaried somewhat from these preferred values without departing from theinvention. Preferably c_(1S) is in the range of 85±10 and c_(2S) is inthe range of −4.7±1. Preferably c_(1D) is in the range 50±10 and c_(2D)is in the range of −4.3±1. It will be appreciated that these constantswill vary depending upon the units in which P and T are expressed.

It can be seen that the unexpected correlation between a and b ofequation (5) permits system 10 to be calibrated for either systolic ordiastolic blood pressure measurements with a single blood pressuremeasurement made by any alternative reliable method. This calibrationprocess can be done by taking a single reliable measurement of thesubjects blood pressure (reference blood pressure, P₀) and acorresponding pulse transit time (reference pulse transit time, T₀) andcalculating the values of a and b for the subject as follows:$\begin{matrix}{a = {c_{1} + \frac{c_{2}\left( {P_{0} - c_{1}} \right)}{{\ln \left( T_{0} \right)} + c_{2}}}} & (9) \\{b = \frac{P_{0} - c_{1}}{{\ln \left( T_{0} \right)} + c_{2}}} & (10)\end{matrix}$

where P₀ is obtained with a reference blood pressure device; T₀ is themeasured elapsed time (either T_(S) or T_(D)) between the detection of apulse at L1 and the detection of the pulse at L2; and c₁ and c₂ are asgiven above.

System 10 may include an input (not shown) for receiving a signalindicative of the reference blood pressure or P₀ may be measured using aseparate device and entered into system 10 by way of either a datacommunication interface, or a manual interface (e.g. a keyboard). Areference blood pressure measuring device may also be integrated withsystem 10.

After system 10 has been calibrated for a particular subject and for aparticular pair L1 and L2 of sensor locations then the subject'ssystolic and diastolic blood pressures can be continuously estimated byfrequently measuring T_(S) and T_(D), as described above and computingestimated systolic and diastolic blood pressures through the use of thefollowing equation: $\begin{matrix}{P = {c_{1} + \frac{c_{2}\left( {P_{0} - c_{1}} \right)}{{\ln \left( T_{0} \right)} + c_{2}} + {\frac{P_{0} - c_{1}}{{\ln \left( T_{0} \right)} + c_{2}}{{\ln (T)}.}}}} & (11)\end{matrix}$

System 10 can then display the subject's estimated blood pressure on asuitable display 54 (FIG. 11), can compare the subject's estimated bloodpressure to one or more stored alarm limits and trigger an alarm signalif the estimated blood pressure exceeds or is less than a particularalarm limit, can periodically record the estimated blood pressure(s) forthe subject and so on.

Those skilled in the art will understand that equation (5) may beclosely approximated by various alternative equations. For example, therelationship between P and T may be represented over a suitable range ofvalues of P by one of the following equations (where α, β, δ and λ areconstant parameters):

P=αT ^(−β)  (12)

P=δe ^(−λT)  (13)

The values for the constant parameters in equations (12) and (13) orsimilar equations may be determined by performing a calibration usingexperimental data. This may be accomplished, for an individual subjectby measuring several pairs of P and T values under conditions such thatthe subjects' blood pressure is not the same during all of the pairs ofmeasurements. The equation in question can then be fit to the data usinga suitable fitting technique such as least-squares fitting.

In general, the parameters of equation (12) (or (13)) are related to oneanother. This fact can be urged to permit single-point calibration of adevice which uses one of these equations, or a similar equation, tomodel the relationship between P and T. The relationship may be derived,for example, by performing calibrations as described in the precedingparagraph, for a significant number of subjects, generating a scatterplot of points (α, β) (or (δ, λ)) and then fitting a curve to theresulting scatter of point. The cure can subsequently used to predictthe value of one of the parameters given a value for the other one ofthe parameters.

When the values of the constants in Equation (5) (or one of equations(12) and (13)) have been determined (Parameters in equations (12) and(13) may be calibrated from a single or multiple reference bloodpressure measurements), then an estimated value for P may be obtained bysubstituting the measured value for T into the appropriate equation.

In some cases performing calibration as described above can produceerroneous results. This is because no measurement of both a referenceblood pressure and a corresponding reference pulse transit time can beprecisely accurate. Errors in the values measured for the referenceblood pressure and reference pulse transit time may result insignificant errors in the values computed for the parameters a and b.

The inventors have discovered that there is a sufficiently goodcorrelation between the parameter b of Equation (5) and the pulsetransit time for use in calibration. This correlation is illustrated inFIGS. 7 and 8. The curves of FIGS. 7 and 8 may be generated by:obtaining multiple P-T data points for each of a number of subjects;obtaining accurate values of a and b by fitting a “best” logarithmictrend line (Equation (5′) to the P-T data points (which may berepresented in a scatter chart) for each individual subject; plotting bas a function of T_(a) for selected subjects (for whom R-squared valuesfor “best” logarithmic trend lines are greater than a suitable valuesuch as 0.5), where T_(a) is the initial pulse transit timecorresponding to the reference blood pressure or the average of allpulse transit time values for each individual subject, and then fittinga suitable curve to the resulting points b-T_(a) (which may berepresented in a scatter chart). It has been found that good results canbe obtained when the fitted curve is a “best” linear trend line,

b=c ₃ T+c ₄.

While the linear relationship between the value for b and the pulsetransit time T_(a) is not perfect it is sufficient to permit calibrationof system 10. It can be seen from FIGS. 7 and 8 that the relationshipbetween b and T_(a) is reasonably linear (pairs of b and T_(a) wereselected with R-squared values for “best” P-T trend lines are typicallygreater than 0.5). The inventors have found that, for systolic bloodpressure, the b-T relationship can be expressed as:

b=−0.4381T _(a)−9.1247  (15)

(i.e. c_(3S)=−0.4381, c_(4S)=−9.1247).

For diastolic blood pressure, the inventors have found that the b-Trelationship can be expressed as:

b=−0.2597T _(a)−4.3789  (18)

(i.e. c_(3D)=−0.2597, c_(4D)=−4.3789).

Accordingly, some embodiments of the invention achieve calibration bydetermining the parameter b (of Equation (5)) from the measuredreference differential pulse transit time T₀ according to theappropriate one of Equations (14) and (15). Then, the other parameter ais obtained based on both the reference blood pressure and referencedifferential pulse transit time (P₀, T₀) and the relationship ofEquation (5).

In particular, a may be obtained as follows:

a=P ₀ −b ln(T ₀)=P ₀−(c ₃ T ₀ +c ₄)ln(T ₀)  (16)

After system 10 has been calibrated for a particular subject and for aparticular pair L1 and L2 of sensor locations using one of the abovemethods, the subject's systolic and diastolic blood pressures can becontinuously estimated by frequently measuring T_(S) and T_(D), asdescribed above, and computing estimated systolic and diastolic bloodpressures through the use of the following equation: $\begin{matrix}\begin{matrix}{P = {P_{0} - {\left( {{c_{3}T_{0}} + c_{4}} \right){\ln \left( T_{0} \right)}} + {\left( {{c_{3}T_{0}} + c_{4}} \right){\ln (T)}}}} \\{= {P_{0} + {\left( {{c_{3}T_{0}} + c_{4}} \right){\ln \left( {T/T_{0}} \right)}}}}\end{matrix} & (17)\end{matrix}$

After the values of the parameters which define the relationship betweenT and P have been determined, it is not necessary to actually calculatethe results of an equation every time that it is desired to make a newmeasurement of P. After appropriate values for the applicable constantshave been determined then any of the above equations can be representedby storing values for P in a lookup table so that the value for P whichcorresponds to a measured value for T can be obtained by looking up themeasured value for T in the lookup table.

Computer software or hardware that uses equation (5), a mathematicalequivalent of equation (5), an alternative equation which relates P andT in substantially the same manner as equation (5) (such as one ofequations (12) or (13)), or a lookup table to obtain a pre-computedvalue for P from a corresponding value for T may be called a “bloodpressure estimation means”.

FIG. 9 illustrates a method 100 that may be implemented in device 26 forderiving an estimated blood pressure from first and second pulse signals16 and 18 device 26 executes software instructions which direct device26 to request digitized signals 16 and 18 (block s1). Block s1 mayinvolve device 26 sending a request via interface 25 to ADC system 24requesting that ADC system 24 obtain and forward by way of interface 25digitized signals 16 and 18.

In block s2 device 26 is directed to determine T_(S) and T_(D) bycomparing digitized signals 16 and 18. Block s2 preferably involvescomputing cross-correlations from signals 16 and 18 as described above.

In block s3, device 26 is directed to determine whether it hascalibration information for the current subject. If so then method 100continues at block s5 if not then method 100 proceeds to block s4 inwhich device 26 runs computer instructions which cause device 26 toobtain calibration information for the current subject. Such calibrationinformation may be obtained, for example, by requesting and obtaininginformation identifying a file accessible to device 26 in whichcalibration information for the subject in question gas been storedpreviously or by requesting input values for measured systolic anddiastolic blood pressure from which the values for b can be calculatedas described above.

System 10 may include a separate sub-system (not shown) for obtainingreference blood pressure values for calibration purposes. If so,calibration block s4 may include reading a reference blood pressurevalue from such a sub-system. In the alternative, reference bloodpressure valued may be entered on a keypad or other user interface.

In block s5 device 26 runs computer instructions which cause it toobtain systolic and diastolic blood pressure estimates from the measuredtime delay (T_(S) or T_(D)) using equation (5) above (or an equivalent)and the values for a and b determined in block s4.

In block s6 device 26 is directed to display computed blood pressureestimates on a suitable display connected to device 26. Block 26preferably includes saving the blood pressure estimate(s) in a file,and/or otherwise making the blood pressure estimates available for use.

In block s7 data processing device 26 runs computer instructions whichdetermine whether the blood pressure monitoring should continue. Blocks7 may include a user selectable delay so that a user can decide howfrequently a new blood pressure estimate will be obtained. If device 26determines in block s7 that a further blood pressure estimate should beobtained then method 100 continues to block s1. If device 26 determinesin block s7 that a further blood pressure estimate should not beobtained then method 100 terminates and device 26 awaits further userinstructions.

Method 100 may be implemented by running suitable computer software on apersonal computer, micro-controller, or other suitable computer device.The computer device may comprise multiple processors. Different steps inmethod 100 may be performed on different processors.

Method 100 could also be completely implemented in hardware. Forexample, circuitry for implementing the methods of the invention couldbe provided on a field programmable gate array (“FPGA”) or anapplication specific integrated circuit (“ASIC”). Apparatus according tothe invention may be integrated within a device which performsadditional functions. For example, signals 16 and/or 18 could be used toprovide data for pulse oximetry determinations and/or pulse ratedeterminations.

FIG. 10 illustrates a possible software architecture for software 50 tobe run on a device 26 in the practice of this invention. A form viewobject 52 provides a graphical display 54 which may, for example, havethe appearance shown in FIG. 11. Display 54 provides a graphical userinterface by way of which a user can control the operation of system 10and see the blood pressure estimates developed by system 10. Display 54includes a portion 55A for displaying estimated systolic blood pressure,a portion 55B for displaying estimated diastolic blood pressure; aportion 55C for displaying the subject's measured heart rate; and aportion 55D for displaying the number of elapsed blood pressuremeasurement cycles. Portions 55E and 55F show digitized signals 16 and18. Portion 55G displays status information. Portion 55H displays thecurrent system date and time.

Display 54 may include a number of user controls including a control 56Afor setting the cycle time; a control 56B for starting a sequence ofblood pressure estimations; a control 56C for reviewing previouslyrecorded blood pressure estimates for the same subject; a portion 57 forsetting and displaying the name of the subject being monitored.

A serial communication object 55 sends commands to ADC unit 24 andreceives data from ADC unit 24 via interface 25.

A blood pressure calculation object 56 processes digitized signals 16and 18 to derive blood pressure estimates, as described above.

A calibration object 58 receives measured blood pressure information andcomputes parameter values for use in calculating a subject's bloodpressure as described above. Calibration object 58 includes, or hasaccess to, calibration information (such as the relationship of Equation(6)).

A file management object 59 moderates the storage of data in files andthe retrieval of data from files accessible to device 26.

A data pre-processing object 60 formats the data to be presented in apredefined format, for example a format compatible with applicationsoftware such as Microsoft™ EXCEL™.

Preferred implementations of the invention comprise a computer processorrunning software instructions which cause the computer processor toperform a method of the invention. The invention may also be provided inthe form of a program product. The program product may comprise anymedium which carries a set of computer-readable signals containinginstructions which, when run by a computer, cause the computer toexecute a method of the invention. The program product may be in any ofa wide variety of forms. The program product may comprise, for example,physical media such as magnetic data storage media including floppydiskettes, hard disk drives, optical data storage media including CDROMs, DVDs, electronic data storage media including ROMs, flash RAM, orthe like or transmission-type media such as digital or analogcommunication links.

As will be apparent to those skilled in the art in the light of theforegoing disclosure, many alterations and modifications are possible inthe practice of this invention without departing from the spirit orscope thereof. For example, Accordingly, the scope of the invention isto be construed in accordance with the substance defined by thefollowing claims.

We claim:
 1. A method for monitoring blood pressure, the methodcomprising: a) detecting a first pulse signal at a first location on asubject and detecting a second pulse signal at a second location on thesubject; b) measuring a reference blood pressure P₀ and a correspondingtime difference T₀ between the first and second pulse signals; c) fromthe reference blood pressure and corresponding time difference,determining a first plurality of constant parameters in amulti-parameter equation relating blood pressure and thetime-difference; d) monitoring the subject's blood pressure byperiodically measuring a time difference T between the first and secondpulse signals; and, e) computing an estimated blood pressure, P, fromthe time difference, T, using the multi-parameter equation and the firstplurality of constant parameters wherein the multi-parameter equation isthe calculation: P=a+bln(T)  or a mathematical equivalent thereof, wherea and b are constants.
 2. The method of claim 1 wherein determining theplurality of constant parameters in the multi-parameter equationcomprises performing calculations mathematically equivalent to:$a = {c_{1} + \frac{c_{2}\left( {P_{0} - c_{1}} \right)}{{\ln \left( T_{0} \right)} + c_{2}}}$${and},{b = \frac{P_{0} - c_{1}}{{\ln \left( T_{0} \right)} + c_{2}}}$

to obtain values for the constants a and b, where c₁ and c₂ arepredetermined constants.
 3. The method of claim 1 wherein the pluralityof constant parameters comprise a first parameter a and a secondparameter b and determining the plurality of constant parameters in themulti-parameter equation comprises performing calculationsmathematically equivalent to: a=P ₀−(c ₃ T ₀ +c ₄)ln(T ₀) and, b=c ₃ T ₀+c ₄ where c₃ and c₄ are predetermined constants.
 4. A method formonitoring blood pressure, the method comprising: a) detecting a firstpulse signal at a first location on a subject and detecting a secondpulse signal at a second location on the subject; b) measuring areference blood pressure P₀ and a corresponding time difference T₀between the first and second pulse signals; c) from the reference bloodpressure and corresponding time difference, determining a firstplurality of constant parameters in a multi-parameter equation relatingblood pressure and the time-difference; d) monitoring the subject'sblood pressure by periodically measuring a time difference T between thefirst and second pulse signals; and, e) computing an estimated bloodpressure, P, from the time difference, T, using the multi-parameterequation and the first plurality of constant parameters wherein themulti-parameter equation comprises a non-linear function which isgenerally decreasing and concave upward in a manner specified by theconstant parameters.
 5. The method of claim 4 wherein the function ismonotonically decreasing.
 6. A method for monitoring blood pressure, themethod comprising: a) detecting a first pulse signal at a first locationon a subject and detecting a second pulse signal at a second location onthe subject; b) measuring a reference blood pressure P₀ and acorresponding time difference T₀ between the first and second pulsesignals; c) from the reference blood pressure and corresponding timedifference, determining a first plurality of constant parameters in amulti-parameter equation relating blood pressure and thetime-difference; d) monitoring the subject's blood pressure byperiodically measuring a time difference T between the first and secondpulse signals; and, e) computing an estimated blood pressure, P, fromthe time difference, T, using the multi-parameter equation and the firstplurality of constant parameters wherein the multi-parameter equation isthe calculation: ti P=αT ^(−β)  or a mathematical equivalent thereofwhere α and β are constants.
 7. A method for monitoring blood pressure,the method comprising: a) detecting a first pulse signal at a firstlocation on a subject and detecting a second pulse signal at a secondlocation on the subject; b) measuring a reference blood pressure P₀ anda corresponding time difference T₀ between the first and second pulsesignals; c) from the reference blood pressure and corresponding timedifference, determining a first plurality of constant parameters in amulti-parameter equation relating blood pressure and thetime-difference; d) monitoring the subject's blood pressure byperiodically measuring a time difference T between the first and secondpulse signals; and, e) computing an estimated blood pressure, P, fromthe time difference, T, using the multi-parameter equation and the firstplurality of constant parameters wherein the multi-parameter equation isthe calculation: P=δe ^(−λT)  or a mathematical equivalent thereof whereδ and λ are constants.
 8. A method for monitoring blood pressure, themethod comprising: a) detecting a first pulse signal at a first locationon a subject and detecting a second pulse signal at a second location onthe subject; b) measuring a reference blood pressure P₀ and acorresponding time difference T₀ between the first and second pulsesignals; c) from the reference blood pressure and corresponding timedifference, determining a first plurality of constant parameters in amulti-parameter equation relating blood pressure and thetime-difference; d) monitoring the subject's blood pressure byperiodically measuring a time difference T between the first and secondpulse signals; and, e) computing an estimated blood pressure, P, fromthe time difference, T, using the multi-parameter equation and the firstplurality of constant parameters wherein the blood pressure is asystolic blood pressure.
 9. A method for monitoring blood pressure, themethod comprising: a) detecting a first pulse signal at a first locationon a subject and detecting a second pulse signal at a second location onthe subject; b) measuring a reference blood pressure P₀ and acorresponding time difference T₀ between the first and second pulsesignals; c) from the reference blood pressure and corresponding timedifference, determining a first plurality of constant parameters in amulti-parameter equation relating blood pressure and thetime-difference; d) monitoring the subject's blood pressure byperiodically measuring a time difference T between the first and secondpulse signals; and, e) computing an estimated blood pressure, P, fromthe time difference, T, using the multi-parameter equation and the firstplurality of constant parameters wherein the method comprises measuringa systolic blood pressure of the subject wherein measuring the timedifference T comprises measuring a first time difference T_(s) forportions of the first and second signals which do not include at leastsome diastolic portions of the signals.
 10. A The method of claim 9comprising additionally measuring a diastolic blood pressure of thesubject by measuring a second time difference T_(D) for portions of thefirst and second pulse signals which do not include at least somesystolic portions of the signals.
 11. The method of claim 10 whereinmeasuring a reference blood pressure comprises measuring a calibrationdiastolic pressure and the method comprises, from the calibrationdiastolic blood pressure and corresponding second time difference T_(D),determining a second plurality of constant parameters in themulti-parameter equation relating blood pressure and the secondtime-difference; and the method comprises monitoring the subject'sdiastolic blood pressure by periodically measuring the second timedifference T_(D) and, computing an estimated diastolic blood pressure,P_(D), from the time difference, T_(D), using the multi-parameterequation and the second plurality of constant parameters.
 12. The methodof claim 9 wherein measuring the first time difference comprisesmaximizing a cross-correlation between the first and second pulsesignals.
 13. The method of claim 12 wherein, in measuring the first timedifference, portions of the first and second pulse signals below a firstthreshold are not considered.
 14. The method of claim 13 wherein thethreshold for the first pulse signal is an average value of the firstpulse signal and the threshold for the second pulse signal is an averagevalue of the second pulse signal.
 15. A method for estimating a bloodpressure of a subject, the method comprising: a) detecting a first pulsesignal at a first location; b) detecting a second pulse signal at asecond location; c) determining an elapsed times, T, between the arrivalof corresponding points of the first and second pulse signals; and, d)computing an estimated blood pressure, P, from the elapsed time byperforming the calculation: P=a+b ln(T)  where a and b are constants.16. The method of claim 15 wherein the corresponding points are peaks ofthe pulse signals.
 17. The method of claim 15 wherein the correspondingpoints are valleys of the pulse signals.
 18. The method of claim 15wherein determining the elapsed time comprises computing across-correlation of the first pulse signal and the second pulse signal.19. The method of claim 18 comprising performing a calibration by takinga reference blood pressure reading to obtain a reference blood pressureP₀ and measuring the elapsed time T₀ corresponding to the referenceblood pressure and performing the calculations:$a = {c_{1} + \frac{c_{2}\left( {P_{0} - c_{1}} \right)}{{\ln \left( T_{0} \right)} + c_{2}}}$${and},{b = \frac{P_{0} - c_{1}}{{\ln \left( T_{0} \right)} + c_{2}}}$

or calculations substantially equivalent thereto to obtain values forthe parameters a and b.
 20. The method of claim 18 comprising performinga calibration by taking a reference blood pressure reading to obtain areference blood pressure P₀ and measuring the elapsed time T₀corresponding to the reference blood pressure and performing thecalculations: a=P ₀−(c ₃ T ₀ +c ₄)ln(T ₀) and, b=c ₃ T ₀ +c ₄ orcalculations substantially equivalent thereto where c₃ and c₄ arepredetermined constants.
 21. A method for estimating the blood pressure,P, of a subject, the method comprising: a) detecting a first pulsesignal at a first location on the subject; b) detecting a second pulsesignal at a second location on the subject; c) performing a calibrationby measuring the subject's blood pressure P₀ and measuring acorresponding elapsed time, T₀, between the arrival of correspondingpoints of the first and second pulse signals; d) subsequently monitoringthe subject's blood pressure by determining an elapsed time, T, betweenthe arrival of corresponding points of the first and second pulsesignals; and, e) calculating an estimated blood pressure, P, based onthe value:$\frac{\left( {P_{0} - c_{1}} \right)}{\left( {{\ln \left( T_{0} \right)} + C_{2}} \right)}$

 where c₁ and a₂ are constants.
 22. The method of claim 21 whereincalculating the estimated blood pressure comprises performing thecomputation:$P = {c_{1} + \frac{c_{2}\left( {P_{0} - c_{1}} \right)}{{\ln \quad \left( T_{0} \right)} + c_{2}} + {\frac{P_{0} - c_{1}}{{\ln \quad \left( T_{0} \right)} + c_{2}}\ln \quad (T)}}$

or a substantially mathematically equivalent computation.
 23. The methodof claim 22 wherein c₁ is about 85.41, and c₂ is about −4.73 forsystolic pressure measurements.
 24. The method of claim 23 wherein c₁ isabout 49.36 and c₂ is about −4.3 for diastolic pressure measurements.25. The method of claim 23 wherein c₁ is in the range of 85±10 and c₂ isin the range of −4.7±1 for systolic pressure measurements.
 26. Themethod of claim 23 wherein c₁ is in the range of 50±10 and c₂ is in therange of −4.3±1 for diastolic pressure measurements.
 27. The method ofclaim 23 where c₁ and c2 are derived by: for several subjects, at eachof two or more times, measuring a reference blood pressure value P₀ anda corresponding elapsed time, T₀, between corresponding points of thefirst and second pulse signals; for each of the subjects determiningbest fit values for a and b such that: P=a+bln(T)  for the measuredreference blood pressure values find elapsed times; based upon thevalues for a and b determining best fit values for c₁ and c₂ such that:a=c ₁ +c ₂ b.
 28. A method for estimating the blood pressure, P, of asubject, the method comprising: a) detecting a first pulse signal at afirst location on the subject; b) detecting a second pulse signal at asecond location on the subject; c) performing a calibration by measuringthe subject's blood pressure P₀ and measuring a corresponding elapsedtime, T₀, between the arrival of corresponding points of the first andsecond pulse signals; d) subsequently monitoring the subject's bloodpressure by determining an elapsed time, T, between the arrival ofcorresponding points of the first and second pulse signals; and, f)calculating and estimated blood pressure, P, substantially according tothe equation: P=P ₀+(c ₃ T ₀ +c ₄)ln(T/T ₀)  where c₃ and c₄ areconstants.
 29. The method of claim 28 wherein c₃ is about −0.4381 and c₄is about −9.1247 for systolic pressure measurements.
 30. The method ofclaim 28 wherein c₃ is about −0.2597 and c₄ is about −4.3789 fordiastolic pressure measurements.
 31. The method of claim 28 wherein c₃is in the range of −0.4381±0.1 and c₄ is in the range of −9.1247±1.2 forsystolic pressure measurements.
 32. The method of claim 28 wherein c₃ isin the range of −0.2597±0.1 and c₄ is in the range of −4.3789±1.0 fordiastolic pressure measurements.
 33. The method of claim 28 where c₃ andc₄ are derived by: for several subjects, at each of two or more times,measuring a reference blood pressure value P₀ and a correspondingelapsed time, T₀, between corresponding points of first and second pulsesignals detected at first and second locations on the subject; for eachof the subjects determining best fit values for a and b such that:P=a+bln(T)  for the measured reference blood pressure values and elapsedtimes; based upon the values for b and an initial pulse transit time oran average pulse transit time, T_(a), determining best fit values for c₃and c₄ such that: b=c ₃ T _(a) +c ₄.
 34. Apparatus for estimating ablood pressure of a subject, the apparatus comprising: a) a computerprocessor; b) an input for receiving a first signal corresponding to apulse signal detected at a first location; c) an input for receiving asecond signal corresponding to the pulse signal detected at a secondlocation; d) a program store containing computer software comprisinginstructions which, when run on the processor cause the processor tomeasure an elapsed time, T, between corresponding points on the firstand second signals and compute an estimated blood pressure, P, from theelapsed time by performing the calculation: P=a+b ln(T)  where a and bare constants.
 35. The apparatus of claim 34 wherein the correspondingpoints correspond to the valleys of the pulse signals for a diastolicblood pressure estimation.
 36. The apparatus of claim 34 wherein thecorresponding points correspond to the peaks of the pulse signals for asystolic blood pressure estimation.
 37. The apparatus of claim 34wherein the software comprises a set of instructions which cause thecomputer processor to compute a cross-correlation of the first andsecond signals.
 38. The apparatus of claim 37 comprising an input forreceiving a reference signal indicative of a reference blood pressurevalue.
 39. Apparatus for estimating a blood pressure of a subject, theapparatus comprising: a) signal detection means for detecting first andsecond pulse signals; b) correlation means for determining an elapsedtime, T, between the first and second pulse signals; c) computationmeans for computing an estimated blood pressure, P, from the elapsedtime according to a non-linear function which is generally decreasingand concave upward in a manner specified by two or more settableparameters; and, d) calibration means for receiving a reference bloodpressure and associating the reference blood pressure with an elapsedtime determined by the correlation means; and, e) means responsive tothe calibration means for establishing values for the two or moresettable parameters from the reference blood pressure and elapsed time.40. The apparatus of claim 39 wherein the non-linear function ismonotonical decreasing.
 41. The apparatus of claim 39 wherein thecalculation means performs the calculation: P=a+b ln(T) where a and bare the settable parameters.
 42. The apparatus of claim 39 wherein thecorrelation means determines separate first and second time differencesT_(S) and T_(D) respectively from higher and lower portions of the firstand second pulse signals respectively.
 43. The apparatus of claim 42wherein the computation means comprises diastolic blood pressurecomputation means for computing a diastolic blood pressure from thefirst time difference and systolic blood pressure computation means forcomputing a systolic blood pressure from the second time difference. 44.The apparatus of claim 39 wherein the correlation means comprises abuffer for holding a segment of the first pulse signal, a buffer forholding a segment of the second pulse signal and a processor executinginstructions which cause the processor to determine a time differencefor which a cross correlation between the segment of the first pulsesignal and the segment of the second pulse signal is maximized.
 45. Theapparatus of claim 44 wherein the correlation means determines separatefirst and second time differences T_(S) and T_(D) respectively fromhigher and lower portions of the first and second pulse signalsrespectively.
 46. The apparatus of claim 45 wherein the correlationmeans comprises means for computing an average value of each of thefirst and second pulse signals and the higher portions comprise portionshaving a value in excess of the average value.
 47. The apparatus ofclaim 44 wherein the correlation means comprises means for creating fromthe first and second pulse signals a first set of modified signals p₁(t)and p₂(t) which include the peaks of the first and second pulse signalsbut do not include valleys of the first and second pulse signals and thecorrelation means determines a first time difference T_(S) bydetermining a time shift which yields a maximum correlation betweensignals of the first set of modified signals.
 48. A program productcomprising a medium bearing computer-readable signals, the signalscontaining instructions which, when executed on a computer processor,cause the computer processor to perform a method for monitoring bloodpressure, the method comprising: a) detecting a first pulse signal at afirst location on a subject and detecting a second pulse signal at asecond location on the subject; b) measuring a reference blood pressureP₀ and a corresponding time difference T₀ between the first and secondpulse signals; c) from the reference blood pressure and correspondingtime difference, determining a first plurality of constant parameters ina multi-parameter equation relating blood pressure and thetime-difference; d) monitoring the subject's blood pressure byperiodically measuring a time difference T between the first and secondpulse signals; and, e) computing an estimated blood pressure, P, fromthe time difference, T, using the multi-parameter equation and the firstplurality of constant parameters.
 49. A method for obtaining a valuerepresenting a blood pressure of a subject, the method comprising:measuring a reference blood pressure P₀ and determining a correspondingreference time difference, T₀ by at least: receiving a first pulsesignal detected at a first location on the subject; receiving a secondpulse signal detected at a second location on the subject; and,determining the reference time difference, T₀, by measuring a time shiftbetween corresponding points of the first and second pulse signals;based upon the reference blood pressure and the reference timedifference, obtaining a non-linear function relating blood pressure andtime difference for the subject; and, at one or more subsequent times,computing an estimated blood pressure, P, by at least: at the one ormore subsequent times, determining a time difference, T, betweencorresponding points of the first and second pulse signals and computingthe non-linear function of the time difference wherein obtaining thenon-linear function comprises determining at least two parameters of thenon-linear function.
 50. The method of claim 49 wherein obtaining thenon-linear function comprises determining a first one of the at leasttwo parameters as a predetermined function of the reference timedifference.
 51. The method of claim 50 wherein obtaining the non-linearfunction comprises determining a second one of the at least twoparameters based upon the first one of the at least two parameters thereference blood pressure and the reference time difference.
 52. Themethod of claim 51 wherein the non-linear function comprises alogarithmic function of T and, in the non-linear function, thelogarithmic function of T is multiplied by the first one of theparameters.
 53. The method of claim 52 wherein, the non-linear functioncomprises adding the second one of the parameters to a result.
 54. Themethod of claim 51 wherein obtaining the first parameter comprisesperforming the calculation b=c ₃ T ₀ +c ₄ where b is the first parameterand c₃ and c₄ are predetermined constants, or a calculationmathematically equivalent thereto.
 55. The method of claim 54 whereinobtaining the second parameter comprises performing the calculation: a=P₀ −bln(T₀) where a is the second parameter, or a calculationmathematically equivalent thereto.
 56. The method of claim 50 whereinthe predetermined function is a function obtained by: collectingmultiple pairs of reference time difference and reference blood pressurefor each of a plurality of reference subjects; for each of the pluralityof reference subjects fitting the non-linear function to the multiplepairs of reference time difference and reference blood pressure toobtain values for the first and second parameters for each of theplurality of reference subjects; and, fitting a suitable curve to obtainthe predetermined function.
 57. The method of claim 56 wherein thesuitable curve comprises a linear trend line.
 58. The method of claim 57wherein the plurality of reference subjects is selected by pickingreference subjects for whom a measure of fit between the non-linearfunction and the multiple pairs of reference time difference andreference blood pressure exceeds a threshold.
 59. The method of claim 58wherein the measure of fit comprises an R-squared value.
 60. A methodfor obtaining a value representing a blood pressure of a subject, themethod comprising: measuring a reference blood pressure P₀ anddetermining a corresponding reference time difference, T₀ by at least:receiving a first pulse signal detected at a first location on thesubject; receiving a second pulse signal detected at a second locationon the subject; and, determining the reference time difference, T₀, bymeasuring a time shift between corresponding points of the first andsecond pulse signals; based upon the reference blood pressure and thereference time difference, obtaining a non-linear function relatingblood pressure and time difference for the subject; and, at one or moresubsequent times, computing an estimated blood pressure, P, by at least:at the one or more subsequent times, determining a time difference, T,between corresponding points of the first and second pulse signals andcomputing the non-linear function of the time difference wherein thenon-linear function comprises a logarithmic function of T.
 61. A methodfor obtaining a value representing a blood pressure of a subject, themethod comprising: measuring a reference blood pressure P₀ anddetermining a corresponding reference time difference, T₀ by at least:receiving a first pulse signal detected at a first location on thesubject; receiving a second pulse signal detected at a second locationon the subject; and, determining the reference time difference, T₀, bymeasuring a time shift between corresponding points of the first andsecond pulse signals; based upon the reference blood pressure and thereference time difference, obtaining a non-linear function relatingblood pressure and time difference for the subject; and, at one or moresubsequent times, computing an estimated blood pressure, P, by at least:at the one or more subsequent times, determining a time difference, T,between corresponding points of the first and second pulse signals andcomputing the non-linear function of the time difference wherein thevalue representing a blood pressure of a subject represents a systolicblood pressure of the subject and the corresponding points on the firstand second signals are in parts of the first and second signalscorresponding to a systolic portion of the subject's pulse.
 62. A methodfor obtaining a value representing a blood pressure of a subject, themethod comprising: measuring a reference blood pressure P₀ anddetermining a corresponding reference time difference, T₀ by at least:receiving a first pulse signal detected at a first location on thesubject; receiving a second pulse signal detected at a second locationon the subject; and, determining the reference time difference, T₀, bymeasuring a time shift between corresponding points of the first andsecond pulse signals; based upon the reference blood pressure and thereference time difference, obtaining a non-linear function relatingblood pressure and time difference for the subject; and, at one or moresubsequent times, computing an estimated blood pressure, P, by at least:at the one or more subsequent times, determining a time difference, T,between corresponding points of the first and second pulse signals andcomputing the non-linear function of the time difference wherein thenon-linear function comprises a logarithmic function of T.
 63. A methodfor obtaining a value representing a blood pressure of a subject, themethod comprising: measuring a reference blood pressure P₀ anddetermining a corresponding reference time difference, T₀ by at least:receiving a first pulse signal detected at a first location on thesubject; receiving a second pulse signal detected at a second locationon the subject; and, determining the reference time difference, T₀, bymeasuring a time shift between corresponding points of the first andsecond pulse signals; based upon the reference blood pressure and thereference time difference, obtaining a non-linear function relatingblood pressure and time difference for the subject; and, at one or moresubsequent times, computing an estimated blood pressure, P, by at least:at the one or more subsequent times, determining a time difference, T,between corresponding points of the first and second pulse signals andcomputing the non-linear function of the time difference wherein thevalue representing a blood pressure of a subject represents a systolicblood pressure of the subject and the corresponding points on the firstand second signals are in parts of the first and second signalscorresponding to a systolic portion of the subject's pulse.